The strong light–matter interaction of a cavity electric field with the dipole moments of an optical transition of molecules gives rise to new eigenstates, namely, lower and upper polariton branches.
Due to dissipation processes, it is necessary to compensate fo the losses, which can be done by an external pump.
Usually, an external pump excites polaritons in the upper polariton branch and excitons which are not coupled with the cavity modes [1]}, [2]}.
The polaritons of the upper branch and excitons [1]}, [2]} scatter the energy supplied by the pump into the lower polariton branch forming BEC at high enough excitation density.
There are several mechanisms allowing such energy relaxation in polariton systems.
Scattering by electrons [5]}, high-energy optical phonons [6]}, and vibrons in organic materials [1]}, [8]} are among them.
Since non-equilibrium BEC occurs mostly in the lower polariton branch, below we consider the dynamics of the lower polariton branch only.
The energy transfer from the upper polaritons or excitons to the lower polaritons will be described by an effective incoherent pumping.
Such an approximation is reasonable for the majority of experimental realizations [9]}, [10]}, [11]}
